Mass shootings do occasionally happen in schools, as was tragically the case last week. They also sometimes happen in offices (San Bernardino), nightclubs (Orlando), concert venues (Las Vegas and Paris), churches (Sutherland Springs), and other places where people gather.

But mostly, they don’t happen.

So we should be careful, as we consider policies to reduce the frequency and deadliness of these already rare events, to make sure that we don’t create more problems than we fix.

Arming teachers is an overreaction

“Imagine in the middle of this crisis and the SWAT team comes into the building and there’s an adult with a weapon in their hands and the SWAT team doesn’t know who is who and we have an additional tragedy that was unnecessary.”

This is a good reason to oppose arming teachers. But there’s a broader one: Asking teachers to carry firearms and placing the burden on them to mount an armed defence of the school is likely to be distracting, even if we arm only those teachers who voluntarily sign up.

They’re supposed to be there to teach. Giving them an additional job will change their mentality about what they’re there for – for the worse.

The resulting interference with the educational process might be a cost worth bearing if school shootings were common. But they’re not.

Some other ideas do more harm than good

Another mostly bad idea is further “hardening” school campuses against shootings, as the National Rifle Association’s CEO, Wayne LaPierre, suggested, with armed police officers and metal detectors.

Some school districts already feel a particular need to do this – mostly to prevent non-mass shooting violence. But it sends a message that school is a dangerous place, or is like a prison. It should be avoided where possible, which is almost everywhere.

One Stoneman Douglas student at the CNN town hall asked why the government wasn’t giving her a Kevlar vest to wear to school. I certainly understand her pain and why she is afraid. But giving out Kevlar vests at school – or taking other steps that emphasise the idea that a mass shooter might be around the corner – would mostly serve to send the message to other students that they should be scared.

Another mostly bad idea is to impose more mental-health-related restrictions on gun ownership.

The idea here is for the government to figure out, in advance of any crime, who is too dangerous to own a gun. I think this approach is unlikely to work because nearly half of Americans will suffer from a mental illness at some point in their lives, and the vast majority of those people are not a danger to themselves or to others. And I think rules that focus on mental health as a criterion for gun ownership are very likely to create new stigmas around mental illness and even discourage people from seeking treatment lest one of their constitutional rights be revoked.

That rule was written in that flawed manner for a reason: It’s really hard to design a rule that takes guns out of the hands of potentially dangerous mentally ill people without roping in a lot of others who aren’t dangerous.

An increase in stigma, resulting from policies that jump from the existence of a mental illness to the conclusion that the person who has it is dangerous, might be worth accepting if it were true that mass shootings were principally a problem of mentally ill people shooting people. But the colloquial assertion that mass shooters are “crazy” overstates the link between diagnosable mental illness and mass violence.

Not all ideas related to guns and mental health are bad: For example, the federal background-check system should be improved to better enforce the existing law prohibiting people who have been institutionalized from owning guns. This rule is appropriate because institutionalization requires demonstrating that a person poses a danger. But institutionalization is a high bar for a good reason, and most dangerous people are never going to be institutionalized.

So, what should we do?

In general, I am sceptical of the urge to “do something” after a tragedy. There are quite a few ill-conceived laws named after victims of crimes. But there are a number of policy responses to mass shootings that I do think provide clear benefits that exceed their costs.

One option is to impose restrictions on the sort of guns that make mass shootings easier and more deadly.

In general, I have seen this idea as legislatively hopeless, but in the past week Republicans up to and including the president have been expressing openness to certain steps, so it’s worth seeing whether they are willing to follow through.

A small step in this direction would be a legislative ban on bump-stock devices like those used by the Las Vegas shooter. Violence committed with these devices is rare, but they serve no valid purpose for lawful gun owners besides novelty, and prohibiting them would align with the spirit (but not the letter) of existing federal laws heavily restricting the ownership of machine guns.

We could impose limits on the number of bullets that can go in a gun magazine – a step Rubio said he was newly open to on Wednesday – so it is harder for a mass shooter to get off quite so many shots. We could raise the age at which it is legal to purchase a semiautomatic rifle.

At the extreme end, we could prohibit semiautomatic guns altogether. This would be a huge policy change – most handguns sold in the US today are semiautomatic – but it would be the most effective policy to reduce the rate of fire available to shooters. So far, Democrats are reluctant to say out loud that they want to go this route, instead drawing a mostly arbitrary line between “assault weapons” they want to ban and other semiautomatic guns that would remain legal.

And we should consider an idea David French has been promoting – gun-violence restraining orders, in which the relatives and close associates of a potentially dangerous person could go to court with evidence of danger that person poses, seeking an order precautionarily stripping that person of guns.

The idea would be to provide recourse in a case like this one in Florida, where the police were repeatedly warned but found no cause to act in advance of the attack. California has had a law like this since 2016, and with some more time we’ll be able to get a sense of how well it’s working.

We should give ourselves permission to live without fear

One thing all these proposals have in common (with the exception of a full ban on semiautos) is they allow life to go on as normal for almost everyone. There is no need to fundamentally change the school experience, or to view tens of millions of mentally ill people with new suspicion, or to act as if an active shooter is always around the corner.

A ban on all semiautomatics would be a significant imposition on the tens of millions of Americans who own such guns. But it’s also the policy that would be likely to bring the largest safety benefits.

These policies wouldn’t end all mass shootings any more than fire-safety policies prevent all fires or anti-crime policies prevent all crime. But they would make us safer at the margin – in an environment where violent crime is already down sharply from where it was 25 years ago. And they wouldn’t require us to choose to live under the assumption that we are under constant threat of violence.

There is an ethos today – not just around guns – that if you’re not living in a state of perpetual alarm, you’re not being a good citizen. But despite what you sometimes hear about America, a lot of things are good and getting better. Crime is down. Teen pregnancy is down. Traffic fatalities are down a lot over the long run. And our schools are mostly quite safe.

We should strive to make them even safer. But in doing so, we should be mindful of not taking steps that accidentally make things worse – which we might do, if we overstate the threat level.